Optimal critical mass for the two-dimensional keller-segel model with rotational flux terms

Elio Espejo, Hao Wu

Research output: Journal PublicationArticlepeer-review

5 Citations (Scopus)
27 Downloads (Pure)

Abstract

Our aim is to show that several important systems of partial differential equations arising in mathematical biology, fluid dynamics and electrokinetics can be approached within a single model, namely, a Keller-Segel-type system with rotational flux terms. In particular, we establish sharp conditions on the optimal critical mass for having global existence and finite time blow-up of solutions in two spatial dimensions. Our results imply that the rotated chemotactic response can delay or even avoid the blow-up. The key observation is that for any angle of rotation α∈(-π, π], the resulting PDE system preserves a dissipative energy structure. Inspired by this property, we also provide an alternative derivation of the general system via an energetic variational approach.

Original languageEnglish
Pages (from-to)379-394
Number of pages16
JournalCommunications in Mathematical Sciences
Volume18
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Blow-up
  • Chemotaxis
  • Critical mass
  • Dissipative energy structure
  • Global existence
  • Rotational flux

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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